Patches which face a disturbance between the years 2015 and 2040 are the basis for this analysis. As a first step in the exploratory analysis, the data is represented as functions by means of a b-spline basis equivalently as for PFT Tundra, i.e. b-splines of order 6, penalizing the third derivative with a penalization parameter \(\lambda = 1\).
Figure 1 shows the chosen basis representation for Pioneering Needleleaf.
To further analyze the data, a FPCA is run for each of the four scenarios and each of the five PFTs separately. Again, let’s take a look at the two principal components for each scenario of PFT Pioneering Needleleaf. Figure 2 shows the principal components.
For Tundra, we could see huge differences between the Control scenario and the climate scenario. Here however, the principal components for all four scenarios are pretty similar and all reflect the same patterns: high values in the first PC stand for much higher values of above ground carbon than the mean after the 10 first years of the considered time span and vice versa for low values. The second principal component mainly reflects lower values as the mean for higher PC2 scores until a break point and then higher values than the mean, vice versa for lower values of PC2. Note that the time point of the change differs among the scenarios.
For a better understanding and an easier interpretation of the principal components, a VARIMAX rotation is applied. This rotation algorithm may reveal more meaningful components of variation in the data (Ramsay et al. (2009)).
Figure 3 shows the VARIMAX rotated first and second principal components for each scenario.
Here, the VARIMAX rotation mainly influences the end of the time period in the first principal component and the break point in the second PC.
In order to detect possible clusters in the data, i.e. the share of above ground carbon may behave in similar ways for several grid points, the two first principal components are plotted against each other for all considered cases: unrotated (Figure 4) and VARIMAX rotated (Figure 5). The color reflects a rough classifying into regions, here continents.
In Figure 4, a light clustering pattern is visible, especially for the more drastic scenarios. The more drastic the scenario, the smaller the PC1 values.
Rotation does not lead to a substantial difference in PC scores for Pioneering Needleleaf. This was already indicated in Figure 3 as the PCs hardly change in comparison to the unrotated ones.
In order to get a better understanding of the spatial component of the data, Figure 6 shows how the portion of above ground carbon from year 0 to 100 after disturbance develop in each grid cell (patch 1).
We can clearly see major differences between the scenarios and the considered regions. The more drastic the warming scenario, the more and earlier Pioneering Needleleaf is present.